Deck 5: Logarithmic, Exponential, and Other Transcendental Functions

Question 1

Find an equation of the tangent line to the graph of at the point (1,0).

A)
B)
C)
D)
E)

Answer 1

Question 2

Use implicit differentiation to find at the point

A)
B)
C)
D)
E)

Answer 2

Question 3

Write the following expression as a logarithm of a single quantity.

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the slope-intercept equation of the line tangent to the graph of when

A)
B)
C)
D)
E)

Question 5

Find the derivative of the function

A)
B)
C)
D)
E)

Question 6

Determine the x-coordinate(s) of any relative extrema and inflection points of the function

A) relative minimum: inflection point:
B)no relative extrema; inflection point:
C)relative minimum: no inflection points
D)no relative extrema; inflection point:
E)relative maximum: inflection point:

Question 7

What is the domain of the function

A)
B)
C)
D)
E)

Question 8

Find the following limit if it exists: Use when appropriate.

A)
B)
C)
D)
E)

Question 9

Find the derivative of the function

A)
B)
C)
D)
E)

Question 10

Write the following expression as a logarithm of a single quantity.

A)
B)
C)
D)
E)

Question 11

Use implicit differentiation to find

A)
B)
C)
D)
E)

Question 12

Find the derivative of the function

A)
B)
C)
D)
E)

Question 13

Differentiate the function

A)
B)
C)
D)
E)

Question 14

Find the following limit if it exists: Use when appropriate.

A)
B)
C)
D)
E)

Question 15

What is the domain of the function

A)
B)
C)
D)
E)

Question 16

Find the derivative of the function

A)
B)
C)
D)
E)

Question 17

Use implicit differentiation to find

A)
B)
C)
D)
E)

Question 18

Differentiate the function

A)
B)
C)
D)
E)

Question 19

Locate any relative extrema and inflection points of the function Use a graphing utility to confirm your results.

A)relative minimum value: no inflection points
B)relative minimum value: inflection point:
C)relative maximum value: inflection point:
D)relative minimum value: no inflection points
E)relative maximum value: no inflection points

Question 20

Determine the x-coordinate(s) of any relative extrema and inflection points of the function

A) relative minimum: no inflection points
B)relative maximum ; inflection point:
C)no relative maximum or minimum; inflection point:
D)no relative extrema or inflection points.
E) relative minimum: inflection point:

Question 21

Suppose the table below shows the temperature at which a given liquid boils at selected pressures p (pounds per square inch).A model that approximates the data is Find the rate of change of T with respect to p when P = 20.Round
Your answer to two decimal places.

A)
B)
C)
D)
E)

Question 22

Suppose the table below shows the temperature at which a given liquid boils at selected pressures p (pounds per square inch).A model that approximates the data is

A)1
B)0
C)
D)
E)

Question 23

Find

A)
B)
C)
D)
E)

Question 24

Find the solution of the differential equation which passes through the point

A)
B)
C)
D)
E)

Question 25

Suppose the term of a mortgage t (in years) can be approximated by where x is the monthly payment in dollars.Use
The model to approximate the term of a home mortgage for which the monthly payment is What is the total amount paid? Round your answer to the nearest cent.Your answer may be slightly
Different depending on the number of digits your technology uses in computations.

A)
B)
C)
D)
E)

Question 26

Find the indefinite integral

A)
B)
C)
D)
E)

Question 27

Find

A)
B)
C)
D)
E)

Question 28

Suppose the term of a mortgage t (in years) can be approximated by where x is the monthly payment in dollars.Find
The instantaneous rate of change of t with respect to x when Round your answer to four
Decimal places.

A)0.0044
B)-0.1619
C)0.0619
D)-0.0619
E)-0.0044

Question 29

Find the indefinite integral.

A)
B)
C)
D)
E)

Question 30

Find the indefinite integral.

A)
B)
C)
D)
E)

Question 31

Find the indefinite integral.

A)
B)
C)
D)
E)

Question 32

Find the indefinite integral

A)
B)
C)
D)
E)

Question 33

Suppose the table below shows the temperature at which a given liquid boils at selected pressures p (pounds per square inch).A model that approximates the data is Use a graphing utility to graph

A)
B)
C)
D)
E)

Question 34

Find the indefinite integral of

A)
B)
C)
D)
E)

Question 35

Find

A)
B)
C)
D)
E)

Question 36

Use integration to find the particular solution of the differential equation which passes through the point

A)
B)
C)
D)
E)

Question 37

The relationship between the number of decibels and the intensity I of sound in watts per centimeter squared is Determine the number of decibels of a sound
With an intensity of watts per square centimeter.

A)250 decibels
B)65 decibels
C)70 decibels
D) decibels
E)75 decibels

Question 38

Find the solution of the differential equation which passes through the point

A)
B)
C)
D)
E)

Question 39

Use logarithmic differentiation to find the derivative of

A)
B)
C)
D)
E)

Question 40

Find the indefinite integral.

A)
B)
C)
D)
E)

Question 41

Find the area of the region given below bounded by the graph of

A)
B)
C)
D)
E)

Question 42

Find

A)
B)
C)
D)
E)

Question 43

Suppose a population of bacteria is changing at a rate of where t is the time in days.The initial population (when t = 0) is 500.Write an equation that gives the population at
Any time t.

A)
B)
C)
D)
E)

Question 44

Find the time required for an object to cool from by evaluating where t is time in minutes.Round your answer to four decimal places.

A)6.4346 minutes
B)4.4251 minutes
C)3.6907 minutes
D)4.0598 minutes
E)5.8496 minutes

Question 45

Find the area of the region bounded by the graphs of the equations Round your answer to four decimal places.

A)13.6566
B)12.3178
C)12.6566
D)11.3178
E)12.7041

Question 46

Evaluate the definite integral

A)
B)
C)
D)
E)

Question 47

Evaluate the definite integral.

A)
B)
C)
D)
E)

Question 48

Evaluate

A)
B)
C)
D)
E)

Question 49

Suppose a population of bacteria is changing at a rate of where t is the time in days.The initial population (when t = 0) is 1,500.Identify an equation that gives the
Population at any time t and use it to find the population when days.Round your answer to the
Nearest integer.

A)12,783
B)11,525
C)13,533
D)10,772
E)11,522

Question 50

Find

A)
B)
C)
D)
E)

Question 51

Find

A)
B)
C)
D)
E)

Question 52

Suppose the demand equation for a product is Find the average price p on the interval Round your answer to the nearest dollar.

A)$67
B)$83
C)$57
D)$565
E)$52